Cooperative Game Theory A transferable utility cooperative G

Cooperative Game Theory

A transferable utility cooperative Game G = (N, v) is called symmetric if v(s) = z(|S|) for some function z : N -> R.

Prove all aspects your conjecture rigorously.

Solution

In the n person game as given in the problem, the main focus is to how the coalition S can provide or distribute the value v(s) to its members in anyway they choose.

Possible Outcomes/ Solutions

An outcome of the game in characteristics form can be determined and consists of

1) Partition of N trails into coalition structures

2) Secondly, the pay-off vectors (in terms of cooperative game theory) that distributes the value of coalition into numbers

If a payoff vector is an imputation, then each player prefers this to bei ng alone. Howver, a group of players may want to deviate since it might be better for them and this would result in unstable conditions